Rebuttals Heralded as “Truth”, Dept.

Barbara Oakley wrote an op-ed in the NY Times, that went against the current faddish and prevalent thinking that math taught in the traditional manner kills all desires to learn math. She advocates learning the foundational aspects of math through practice (derisively referred to as ‘drill’) and cites her own experience learning Russian at the Defense Language Institute–one of the best language learning facilities in the world.

A recent blog post offered a rebuttal to this, which is not unusual if you read the comments to Oakley’s NY Times piece.  People do not like being told that traditional methods of math teaching have merit–particularly when the current “narrative” about traditional math teaching is that it doesn’t work and turns students off of math.  It is portrayed as nothing but drill, rote learning, no connection between concepts and no understanding. Also, they tend to make questionable statements such as this: “Whereas [Oakley] says we have foregone drill and practice for conceptual understanding, our problem in the United States is understood by learning scientists to be precisely the opposite.”

I have had the pleasure of being in contact with Ms Oakley over the past two years and alerted her to the blog.  She tried to post a comment on it but it has not yet appeared.  I don’t wish to assume that the blogger refuses to post it, but instead will just speed things along and post Oakley’s comment here.  As indicated in Oakley’s comment below, there are learning scientists that support her view in contrast to the above quoted statement.

I learned Russian at the Defense Language Institute–one of the best language learning facilities in the world.  The learning practices there included plenty of drill and yes, rote memorization, along with conversation and application.  When I applied those same techniques to learning math when I started trying to learn remedial high school algebra at age 26, it worked beautifully. As well it should, since the Defense Language Institute approach involves virtually all aspects of what we know about how to learn a language–or any subject–well. 

My own daughters received plenty of drill practice of math in the ten years I had them in Kumon mathematics, from ages 3 to 13.  According to the precepts of the above blog post, my daughters should hate math.  Instead, their early wobbly dislike for math turned into expertise and enjoyment–just as with a child who spends not-always-fun time with piano practice can grow into an adult who treasures her ability to play the piano.

The vast majority of my colleagues in engineering are from countries that emphasize rote approaches to learning math.  Their early rote training certainly didn’t kill their desire or ability to excel in analytical topics. Virtually every subject we know of, from language learning to playing an instrument, to learning in math and science, proceeds from a basis of solid mental representations developed through practice and procedural fluency that minimizes cognitive load while maximizing access to neurally embedded information. (See Anders Ericsson’s seminal work on the development of expertise.)

Many schools in the US been strongly discouraged by previous policies of the NCTM from encouraging students to develop any type of procedural fluency or deeply embedded sets of concepts, such as multiplication tables. (Yes, even memorization of multiplication tables helps children to develop pattern as well as number sense.) I still remember the student who came up to me after flunking a statistics test, saying “I just don’t see how I could have flunked this test–I understood it when you said it in class.”  We’ve gone so overboard with the value of conceptual understanding that students think it’s the golden key–they don’t need to practice to build, maintain, or enhance their “understanding.” And of course, what a student thinks they understand is often only a glimmer of the real understanding that comes from plenty of interleaved practice. In reality, procedural fluency and understanding proceed hand-in-hand.  See Rittle-Johnson, B, et al. “Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics.” Educational Psychology Review 27, 4 (2015): 587-597.

Note that the above blog post cites only one-sided articles in support of the author’s message–no mention is made of the researchers and results cited in the original op-ed, or other meaningful, solid research such as the following, that rebuts the author’s assertions. See, for example:

Morgan, PL, et al. “Which instructional practices most help first-grade students with and without mathematics difficulties?” Educational Evaluation and Policy Analysis 37, 2 (2015): 184-205.

[Morgan notes that music, movement, and manipulatives are fun, but the basics, with explicit instruction and plenty of worksheet practice, are best for struggling math students.]

Geary, DC, et al. “Introduction: Cognitive foundations of mathematical interventions and early numeracy influences.” In Mathematical Cognition and Learning, Vol 5: Elsevier, 2019.

Geary, DC, et al. “Developmental Change in the Influence of Domain-General Abilities and Domain-Specific Knowledge on Mathematics Achievement: An Eight-Year Longitudinal Study.” Journal of Educational Psychology 109, 5 (2017): 680-693.

Neuroscience and cognitive psychology are doing a great deal to advance our understanding of what is necessary to excel in a given subject.  I would hope that educators in mathematics would open their eyes to new and relevant insights from these disciplines, and realize that their desire to always make their subject fun (something that teachers of virtually every other subject realize just isn’t possible), results in disempowering the very students they mean to help.

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